Problem: Simplify the following expression: $t = \dfrac{1}{3n} + \dfrac{1}{5n}$
In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $3n$ and $5n$ $\lcm(3n, 5n) = 15n$ $ t = \dfrac{5}{5} \cdot \dfrac{1}{3n} + \dfrac{3}{3} \cdot \dfrac{1}{5n} $ $t = \dfrac{5}{15n} + \dfrac{3}{15n}$ $t = \dfrac{5 +3}{15n}$ $t = \dfrac{8}{15n}$